As an example I think people from the American political left to somewhere(?) in the middle see it as what it has been introduced as, that being looking past the status quo and instead looking at your own values, i.e. the morality of homelessness and not having a disdain for them but empathy for them instead.
and then on the other side it feels like the people on the American political right see it as what this website describes it as “ A self-righteously moralistic person who behaves as if superior to others.”
I think the divide has originated from taking unlikeable behaviour and labeling that as ‘woke’ (in bad faith of course) and some people have just bonded to that definition so much that they see it as that.
At least that’s what I’ve noticed online over the past few (bonkers) years
Many political groups do this: they identify some aspect of the opposition, preferably one that is easy to ridicule, and then repeat those accusations ad-nauseum. The complaints about, say, LatinX have far surpassed the number of actual proponents of it, which were a small number of people of the left. However, it still brought up again and again because it forms a useful image of what people are fighting against.
The trouble with this is that a groups idea of the “enemy” typically outlasts and often surpasses the actual enemy that idea is based off of. People on the right will write endless articles and videos about wokeness not because there actually exists a problem with wokeness but to try to gain political and social status with their political group.
I agree that the number of proponents of something like "LatinX", or "biological males playing women's sports" are far, far outnumbered by the people who aren't supporters of those things. But the issue is that the people who are supporters tend to be extremely vocal and generally in positions of power or better able to influence those who are, whether thats in corporate or academic administration settings. As such the small number of "woke" individuals are having outsized effects on society and culture, and the backlash is in response to the magnitude of that influence, rather than the number of people pushing for it.